If rubber cannot melt, how is it molded (vulcanized?) into tires, o-rings, gaskets, and such? You answered this later in the lecture; sulfur is added to the rubber and then the things are molded, right?

Yes. Vulcanization is done with the object in its final form. The plastic is assembled while it is still thermoplastic; without the cross-links that render it unmeltable. It is then vulcanized into a single giant molecule; a thermoset. This vulcanization may be done with sulfur, as in car tires, or it may be some other reaction. In silicone rubber (e.g. bathtub chalking), the vulcanization occurs spontaneously in air. The polydimethyl siloxane molecules are treated at their ends so that they vulcanize in air, releasing acetic acid (the vinegar smell). The resulting thermoset silicone rubber is one giant molecule and cannot melt any more.